Hybrid Niching-Based Differential Evolution With Two Archives for Nonlinear Equation System
提出一种混合小生境差分进化算法HNDE/2A，结合拥挤和物种形成两种小生境技术，利用根存档和劣质后代存档，在有限计算预算内同时找到多个根，在30个测试问题和两个实际问题中表现优于对比算法。
Nonlinear equation systems (NESs) are ubiquitous, and solving them is an important yet challenging task in numerical computation. Most of the NESs usually contain multiple roots. To locate multiple roots, the use of evolutionary algorithms attracts more attention recently. For the purpose of finding different roots within a limited computational budget in a single run simultaneously, in this article, a hybrid niching-based differential evolution with two archives, referred to as HNDE/2A, is proposed. It can be featured as: 1) two niching techniques, i.e., crowding and speciation, are combined to balance the diversity and convergence; 2) a root archive is used to save the found roots during the run. Additionally, if a root is saved into the root archive, it will be reinitialized immediately to further promote the population diversity; and 3) an inferior offspring archive is presented to utilize the useful information of the inferior offspring. To evaluate the performance of our proposal, 30 problems are chosen as the test suite. Moreover, HNDE/2A is also used to solve two real-world problems. Compared with other algorithms, HNDE/2A yields better results in terms of the root ratio and the success rate with a less computational budget.